The models we currently use to understand aerospace safety and accidents are based on a structuralist vocabulary, with mechanistic metaphors that describe the internal workings or failings of operators and their surrounding organizations. Such a view may be increasingly at odds with interpretative demands posed by recent accidents in otherwise very safe systems. Particularly the drift into failure, which represents a large category of residual risk in aerospace, is hard to model (and thereby understand and predict) with structuralist approaches. Drifting into failure is not so much about breakdowns or malfunctioning of components, but about an organization not adapting effectively to the complexity of its structure and environment. This requires aerospace to adopt a true systems approach, which sees sociotechnical complexity not as constituted of parts and their interactions, but as a web of dynamic, evolving relationships and transactions. This can lead to models that can make processes of drift come alive, and help point to more productive countermeasures.